素环上具有b-广义导数的Engel条件

IF 0.9 4区数学 Q1 Mathematics

Miskolc Mathematical Notes Pub Date : 2023-01-01 DOI:10.18514/mmn.2023.4001

Mohammad Salahuddin Khan, A. Khan

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引用次数: 0

摘要

．设R是一个素环，I是R的一个非零理想，Q是它的最大商环，C是它的扩展质心。本文的目的是说明如果R承认非零b推导广义F这样[F (x) x n + x n F (x), x R] k = 0 x∈,m, n, R, k是固定的正整数,然后存在λ∈C, F (x) =λx除非R∼= m 2 (GF(2)), 2×2矩阵环的伽罗瓦域GF(2)的两个元素。

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An Engel condition with b-generalized derivations in prime rings

. Let R be a prime ring, I be a nonzero ideal of R , Q be its maximal right ring of quotients and C be its extended centroid. The aim of this paper is to show that if R admits a nonzero b -generalized derivation F such that [ F ( x m ) x n + x n F ( x m ) , x r ] k = 0 for all x ∈ I , where m , n , r , k are ﬁxed positive integers, then there exists λ ∈ C such that F ( x ) = λ x unless R ∼ = M 2 ( GF ( 2 )) , the 2 × 2 matrix ring over the Galois ﬁeld GF ( 2 ) of two elements.

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来源期刊

Miskolc Mathematical Notes Mathematics-Algebra and Number Theory

CiteScore

2.00

自引率

0.00%

发文量

期刊介绍： Miskolc Mathematical Notes, HU ISSN 1787-2405 (printed version), HU ISSN 1787-2413 (electronic version), is a peer-reviewed international mathematical journal aiming at the dissemination of results in many fields of pure and applied mathematics.